What is the integral of ln(x/(x^2)) ?

The integral of ln(x/(x^2)) is -xln(x)+x+C

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integral of ln(x/(x^2))

\int ln (\frac{x}{x ^{2}}) d x

- x ln (x) + x + C

Solution steps

\int ln (\frac{x}{x ^{2}}) d x

Simplify

ln (\frac{x}{x ^{2}}) : - ln (x)

= \int - ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int ln (x) d x

Apply Integration By Parts

: x ln (x) - \int 1 d x

= - (x ln (x) - \int 1 d x)

\int 1 d x = x

= - (x ln (x) - x)

Simplify

= - x ln (x) + x

Add a constant to the solution

= - x ln (x) + x + C

f (x) = \frac{cos ( x )}{x}

- cos (3 x) \cdot 3

\int \frac{1}{a x ^{2} + b x} d x

x \to 5 lim (8 x + ∣ x - 5 ∣)

2 sin (π x)

What is the integral of ln(x/(x^2)) ?
The integral of ln(x/(x^2)) is -xln(x)+x+C